The Pi Theorem Revisited: On Representations of Quantity Functions

TL;DR

This paper revisits the Pi theorem by establishing a new representation theorem for regular quantity functions within the framework of quantity spaces, offering fresh insights into dimensional analysis.

Contribution

It introduces a novel representation theorem for regular quantity functions, enhancing the theoretical foundation of the Pi theorem and dimensional analysis.

Findings

Proves a new representation theorem for regular quantity functions.

Provides a fresh perspective on the classical Pi theorem.

Strengthens the theoretical basis of dimensional analysis.

Abstract

This note states and proves a representation theorem for regular quantity functions, based on the theory of quantity spaces, thereby giving a new perspective on dimensional analysis and the classical $\pi$ theorem.